A167347 Totally multiplicative sequence with a(p) = (p-1)*(p-3) = p^2-4p+3 for prime p.

1, -1, 0, 1, 8, 0, 24, -1, 0, -8, 80, 0, 120, -24, 0, 1, 224, 0, 288, 8, 0, -80, 440, 0, 64, -120, 0, 24, 728, 0, 840, -1, 0, -224, 192, 0, 1224, -288, 0, -8, 1520, 0, 1680, 80, 0, -440, 2024, 0, 576, -64

Offset

1,5

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Multiplicative with a(p^e) = ((p-1)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)-3))^e(k).

a(3k) = 0 for k >= 1.

a(n) = A003958(n) * A166589(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 3/p^2 + 1/p^3 - 3/p^4) = 0.06874072991... . - Amiram Eldar, Dec 15 2022

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 1)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)

Crossrefs

Cf. A003958, A166589.

Sequence in context: A028636 A028620 A167300 * A028604 A292531 A337550

Adjacent sequences: A167344 A167345 A167346 * A167348 A167349 A167350

Keyword

sign,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved